## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: CHI_MLU ~ 1 + MOT_MLU
## Data: data (Number of observations: 352)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.06 0.24 -1.53 -0.60 1.00 3854 2714
## MOT_MLU 0.78 0.06 0.66 0.90 1.00 3918 2639
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.77 0.03 0.72 0.83 1.00 4005 2880
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.3186164 0.0334731 0.2497849 0.3804363
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: CHI_MLU ~ 1 + MOT_MLU
## Data: data (Number of observations: 352)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.06 0.24 -1.53 -0.60 1.00 3854 2714
## MOT_MLU 0.78 0.06 0.66 0.90 1.00 3918 2639
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.77 0.03 0.72 0.83 1.00 4005 2880
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.3186164 0.0334731 0.2497849 0.3804363
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: CHI_MLU ~ MOT_MLU + Diagnosis + Visit + Child.ID
## Data: data (Number of observations: 352)
## Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 2000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.80 0.25 -1.31 -0.34 1.00 2607 1722
## MOT_MLU 0.54 0.06 0.41 0.67 1.00 2159 1728
## DiagnosisTD 0.40 0.08 0.24 0.57 1.00 2176 1424
## Visit 0.17 0.02 0.12 0.21 1.00 2161 1398
## Child.ID -0.00 0.00 -0.01 0.00 1.00 2622 1613
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.71 0.03 0.66 0.76 1.00 2293 1354
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.4319807 0.03094327 0.3701946 0.4901642
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: CHI_MLU ~ MOT_MLU * Diagnosis + Visit + MOT_MLU:Visit + Diagnosis:Visit
## Data: data (Number of observations: 352)
## Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 2000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.50 0.50 -1.48 0.50 1.00 1070 1155
## MOT_MLU 0.54 0.14 0.25 0.83 1.00 1021 1167
## DiagnosisTD -0.36 0.51 -1.34 0.66 1.00 1196 1073
## Visit 0.06 0.13 -0.21 0.32 1.00 1035 975
## MOT_MLU:DiagnosisTD -0.01 0.13 -0.28 0.25 1.00 1169 1036
## MOT_MLU:Visit -0.00 0.04 -0.07 0.07 1.00 971 985
## DiagnosisTD:Visit 0.24 0.05 0.14 0.33 1.00 1721 1279
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.68 0.03 0.63 0.74 1.00 1786 1302
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.4732861 0.02745144 0.4171806 0.5217459
## Warning: There were 160 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: CHI_MLU ~ MOT_MLU + Diagnosis + Diagnosis:Visit + (1 | Visit) + (1 | Child.ID) + (1 | Diagnosis)
## Data: data (Number of observations: 352)
## Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 2000
##
## Group-Level Effects:
## ~Child.ID (Number of levels: 61)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.56 0.06 0.46 0.68 1.01 329 632
##
## ~Diagnosis (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.44 1.10 0.07 4.02 1.01 902 795
##
## ~Visit (Number of levels: 6)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.17 0.11 0.06 0.43 1.01 474 658
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.03 1.33 -2.90 2.86 1.00 777 799
## MOT_MLU 0.37 0.05 0.27 0.48 1.00 946 1313
## DiagnosisTD -0.28 1.85 -4.18 3.63 1.01 819 842
## DiagnosisASD:Visit 0.06 0.05 -0.03 0.17 1.00 463 472
## DiagnosisTD:Visit 0.30 0.05 0.20 0.40 1.01 458 459
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.41 0.02 0.38 0.45 1.00 1146 1117
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.8066044 0.01062774 0.7840735 0.8253711
## Warning: There were 327 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: CHI_MLU ~ MOT_MLU + Diagnosis + Diagnosis:Visit + (MOT_MLU + Diagnosis | Visit) + (MOT_MLU | Diagnosis) + (MOT_MLU + Diagnosis + Visit | Child.ID)
## Data: data (Number of observations: 352)
## Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 2000
##
## Group-Level Effects:
## ~Child.ID (Number of levels: 61)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.50 0.24 0.05 0.98 1.00 220
## sd(MOT_MLU) 0.21 0.06 0.11 0.35 1.01 144
## sd(DiagnosisTD) 0.54 0.16 0.23 0.87 1.01 213
## sd(Visit) 0.09 0.02 0.06 0.13 1.01 135
## cor(Intercept,MOT_MLU) -0.62 0.33 -0.96 0.28 1.02 112
## cor(Intercept,DiagnosisTD) 0.26 0.37 -0.52 0.86 1.03 139
## cor(MOT_MLU,DiagnosisTD) -0.68 0.18 -0.94 -0.25 1.01 452
## cor(Intercept,Visit) -0.49 0.32 -0.93 0.26 1.03 88
## cor(MOT_MLU,Visit) 0.37 0.27 -0.16 0.83 1.02 307
## cor(DiagnosisTD,Visit) -0.52 0.24 -0.92 0.00 1.01 371
## Tail_ESS
## sd(Intercept) 388
## sd(MOT_MLU) 442
## sd(DiagnosisTD) 573
## sd(Visit) 241
## cor(Intercept,MOT_MLU) 230
## cor(Intercept,DiagnosisTD) 393
## cor(MOT_MLU,DiagnosisTD) 839
## cor(Intercept,Visit) 270
## cor(MOT_MLU,Visit) 734
## cor(DiagnosisTD,Visit) 801
##
## ~Diagnosis (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 1.88 1.65 0.08 6.16 1.01 1007
## sd(MOT_MLU) 0.56 0.49 0.03 1.80 1.01 333
## cor(Intercept,MOT_MLU) -0.04 0.57 -0.96 0.96 1.01 1402
## Tail_ESS
## sd(Intercept) 1028
## sd(MOT_MLU) 863
## cor(Intercept,MOT_MLU) 1020
##
## ~Visit (Number of levels: 6)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.20 0.22 0.01 0.72 1.01 608
## sd(MOT_MLU) 0.08 0.06 0.01 0.22 1.01 366
## sd(DiagnosisTD) 0.35 0.25 0.09 0.97 1.00 668
## cor(Intercept,MOT_MLU) -0.34 0.49 -0.97 0.78 1.01 712
## cor(Intercept,DiagnosisTD) 0.02 0.49 -0.88 0.88 1.00 569
## cor(MOT_MLU,DiagnosisTD) -0.17 0.42 -0.87 0.72 1.01 1199
## Tail_ESS
## sd(Intercept) 770
## sd(MOT_MLU) 549
## sd(DiagnosisTD) 908
## cor(Intercept,MOT_MLU) 1082
## cor(Intercept,DiagnosisTD) 976
## cor(MOT_MLU,DiagnosisTD) 943
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.61 1.86 -3.67 4.39 1.01 423 883
## MOT_MLU 0.34 0.36 -0.45 1.01 1.01 162 123
## DiagnosisTD -0.97 2.63 -6.67 5.12 1.01 465 866
## DiagnosisASD:Visit 0.06 0.07 -0.09 0.19 1.00 602 525
## DiagnosisTD:Visit 0.29 0.12 0.06 0.52 1.01 723 518
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.34 0.02 0.31 0.38 1.00 362 1096
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.8683146 0.01016479 0.8467115 0.8852524
## Warning: There were 254 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: CHI_MLU ~ MOT_MLU + Diagnosis + Diagnosis:Visit + (MOT_MLU | Diagnosis) + (MOT_MLU + Diagnosis | Visit | Child.ID)
## Data: data (Number of observations: 352)
## Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 2000
##
## Group-Level Effects:
## ~Child.ID (Number of levels: 61)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.65 0.26 0.15 1.14 1.00 379
## sd(MOT_MLU) 0.30 0.07 0.18 0.44 1.00 289
## sd(DiagnosisTD) 0.54 0.15 0.26 0.86 1.00 443
## cor(Intercept,MOT_MLU) -0.82 0.21 -0.99 -0.20 1.01 167
## cor(Intercept,DiagnosisTD) 0.41 0.36 -0.38 0.95 1.00 189
## cor(MOT_MLU,DiagnosisTD) -0.77 0.17 -0.98 -0.35 1.01 311
## Tail_ESS
## sd(Intercept) 326
## sd(MOT_MLU) 347
## sd(DiagnosisTD) 730
## cor(Intercept,MOT_MLU) 259
## cor(Intercept,DiagnosisTD) 357
## cor(MOT_MLU,DiagnosisTD) 734
##
## ~Diagnosis (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 1.80 1.51 0.07 5.81 1.00 996
## sd(MOT_MLU) 0.50 0.45 0.03 1.65 1.01 714
## cor(Intercept,MOT_MLU) -0.05 0.60 -0.96 0.97 1.00 1182
## Tail_ESS
## sd(Intercept) 868
## sd(MOT_MLU) 967
## cor(Intercept,MOT_MLU) 584
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.36 1.66 -3.18 3.94 1.00 1086 849
## MOT_MLU 0.36 0.27 -0.31 0.93 1.01 738 846
## DiagnosisTD -1.09 2.47 -7.04 3.93 1.00 931 618
## DiagnosisASD:Visit 0.07 0.02 0.03 0.11 1.00 1808 1252
## DiagnosisTD:Visit 0.29 0.02 0.25 0.33 1.00 2153 1335
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.39 0.02 0.36 0.43 1.01 1238 1089
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.8234624 0.01069002 0.7998395 0.8431738
multiple_parameters_model <- brms::brm(
brms::bf(
CHI_MLU ~ MOT_MLU + Diagnosis + Diagnosis:Visit + (MOT_MLU|Diagnosis) + (MOT_MLU + Diagnosis|Visit) + (MOT_MLU + Diagnosis + Visit|Child.ID),
sigma ~ MOT_MLU + Diagnosis + (Diagnosis|Visit)),
data = data,
file = 'data/w6/multiple_parameters',
chains = 2,
cores = 2,
seed = 112)## Family: gaussian
## Links: mu = identity; sigma = log
## Formula: CHI_MLU ~ MOT_MLU + Diagnosis + Diagnosis:Visit + (MOT_MLU | Diagnosis) + (MOT_MLU + Diagnosis | Visit) + (MOT_MLU + Diagnosis + Visit | Child.ID)
## sigma ~ MOT_MLU + Diagnosis + (Diagnosis | Visit)
## Data: data (Number of observations: 352)
## Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 2000
##
## Group-Level Effects:
## ~Child.ID (Number of levels: 61)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.50 0.21 0.11 0.94 1.03 83
## sd(MOT_MLU) 0.20 0.06 0.10 0.33 1.10 18
## sd(DiagnosisTD) 0.48 0.16 0.21 0.79 1.01 58
## sd(Visit) 0.09 0.02 0.06 0.13 1.01 161
## cor(Intercept,MOT_MLU) -0.57 0.32 -0.95 0.22 1.09 19
## cor(Intercept,DiagnosisTD) 0.24 0.38 -0.54 0.85 1.04 44
## cor(MOT_MLU,DiagnosisTD) -0.72 0.20 -0.97 -0.24 1.03 67
## cor(Intercept,Visit) -0.50 0.29 -0.91 0.13 1.02 59
## cor(MOT_MLU,Visit) 0.41 0.26 -0.14 0.85 1.01 94
## cor(DiagnosisTD,Visit) -0.51 0.25 -0.90 0.04 1.01 128
## Tail_ESS
## sd(Intercept) 203
## sd(MOT_MLU) 106
## sd(DiagnosisTD) 195
## sd(Visit) 339
## cor(Intercept,MOT_MLU) 135
## cor(Intercept,DiagnosisTD) 186
## cor(MOT_MLU,DiagnosisTD) 118
## cor(Intercept,Visit) 221
## cor(MOT_MLU,Visit) 220
## cor(DiagnosisTD,Visit) 336
##
## ~Diagnosis (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 2.62 2.73 0.05 9.32 1.03 61
## sd(MOT_MLU) 0.55 0.59 0.03 2.06 1.01 208
## cor(Intercept,MOT_MLU) -0.05 0.56 -0.95 0.93 1.02 329
## Tail_ESS
## sd(Intercept) 76
## sd(MOT_MLU) 370
## cor(Intercept,MOT_MLU) 686
##
## ~Visit (Number of levels: 6)
## Estimate Est.Error l-95% CI u-95% CI
## sd(Intercept) 0.24 0.22 0.01 0.75
## sd(MOT_MLU) 0.08 0.06 0.01 0.23
## sd(DiagnosisTD) 0.30 0.21 0.07 0.87
## sd(sigma_Intercept) 0.14 0.13 0.01 0.48
## sd(sigma_DiagnosisTD) 0.28 0.23 0.01 0.86
## cor(Intercept,MOT_MLU) -0.41 0.49 -0.99 0.69
## cor(Intercept,DiagnosisTD) 0.11 0.49 -0.88 0.90
## cor(MOT_MLU,DiagnosisTD) -0.19 0.43 -0.89 0.74
## cor(sigma_Intercept,sigma_DiagnosisTD) -0.01 0.58 -0.95 0.94
## Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.02 89 355
## sd(MOT_MLU) 1.02 96 404
## sd(DiagnosisTD) 1.02 175 362
## sd(sigma_Intercept) 1.01 145 468
## sd(sigma_DiagnosisTD) 1.02 140 84
## cor(Intercept,MOT_MLU) 1.04 58 28
## cor(Intercept,DiagnosisTD) 1.02 152 196
## cor(MOT_MLU,DiagnosisTD) 1.02 397 622
## cor(sigma_Intercept,sigma_DiagnosisTD) 1.01 119 264
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.34 3.05 -9.90 3.90 1.05 61 17
## sigma_Intercept -1.87 0.35 -2.56 -1.17 1.01 411 746
## MOT_MLU 0.38 0.37 -0.25 1.40 1.01 126 148
## DiagnosisTD 0.53 5.47 -6.44 18.70 1.03 56 16
## DiagnosisASD:Visit 0.08 0.07 -0.05 0.21 1.01 174 250
## DiagnosisTD:Visit 0.29 0.10 0.09 0.49 1.01 273 323
## sigma_MOT_MLU 0.21 0.09 0.03 0.39 1.01 365 583
## sigma_DiagnosisTD -0.16 0.18 -0.63 0.14 1.02 269 219
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Estimate Est.Error Q2.5 Q97.5
## R2 0.8621564 0.01224518 0.8348675 0.8826969
## CHI_MLU ~ 1 + MOT_MLU
## prior class coef group resp dpar nlpar lb ub
## (flat) b
## (flat) b MOT_MLU
## student_t(3, 1.9, 2.5) Intercept
## student_t(3, 0, 2.5) sigma 0
## source
## default
## (vectorized)
## default
## default